Actually, even another assumption has to be made, not typically stated, that the host ALWAYS has to show you what is behind a door. What if he only shows you when you have already picked the winner? Maybe he wants you to lose and is trying to trick you into changing. In that case, you should never change.

FFS it was called the Monty Hall problem by name - twice - and it has its own Wikipedia page.

There's really no excuse for not knowing the rules.

There was no wikipedia to look at when I read the MVS column in 1990, and the name Monty Hall didn't give me the correct assumptions to make, having never seen his tv show.

If he shows you a goat you should change doors, if he shows you a car you should change doors (this seems obvious), there is no need to assume the host deliberately picks a goat.

Actually if he picks a random one and shows it to you, and it just happens to be a goat, switching does not increase your chances, they are 50% either way. The showing did boost your original 1/3 shot though (regardless of what you do).

Per wikipedia variants:
"Monty Fall" or "Ignorant Monty": The host does not know what lies behind the doors, and opens one at random that happens not to reveal the car. Switching wins the car half of the time.

The other version I also thought of:
"Monty from Hell": The host offers the option to switch only when the player's initial choice is the winning door. Switching always yields a goat.

Because the answer you 'pick' in your mind could be revealed as a wrong answer and removed, so it isn't using that knowledge of your choice to not remove your random choice.

Yeah in my vague recollection I don't think that I was clear that he is only going to reveal an incorrect door. The picture was actually super helpful. For whatever reason the idea still creates this incredible cognitive dissonance for me but I think I understand it more now.

You guys are both being silly. I don't know why you insist that it isn't perfectly clear.

I love how you guys are going all rules lawyer about this stuff. (said in most officious voice) "Well, the problem is almost always unclearly stated". I get it, it took a bunch of times through the problem being explained before it was clear to you that switching was correct. Fine. That's totally standard. Details are important? Whatever. How about the detail that it was a game show? Then, the next part of the formulation was "the host then shows a goat"?

Here's a description in a piece about famous magazine article. You're bringing your own stuff to the party -- it states
He has revealed a goat. What next? If you think it is 50/50 to stay, please explain why so we can be amused.

This thread now officially sucks. Can we go back to how I've lost more money to bravos1 in prop bets than in poker bets? I think I'm down like an 8/16 BR or something.

We'll need a receipt.

The good thing is that I've recently found out the poker book collection I've been trying to donate/give away is actually worth thousands of dollars, so I am still in action.

Your 40/80 and 80/160 bankrolls are also bored by the 8/16 BR you've gambled away to bravos1. They both think "OK, he lost a few big blinds, now what?"

You'll have to PM me on this topic, maybe I'm back in action.

Do you mean Texas Hold'Em or Omaha Hold'Em? Because it's not clear.

DougL, you actually don't get it at all, and in your last quoted formulation of the problem it still is possible that it could be 50/50, or even that it could be better to stay. Saying "the host is well-aware of what is going on behind the scenes" doesn't imply that he always shows a door or that he always picks a goat to show. Have you actually read the original question as written?

Yeah I mean. If you don't get it from the Wikipedia article no explanation here is gonna help.

Problem solving tip always take it to the extememes (zero or a million) and the answer usually becomes clearer.

Trust me captain rs bankroll isn't bored.

Like if you have a problem with your girlfriend, just imagine what happens if you have zero girlfriends or a million girlfriends and then the answer is usually clearer.

this has happened to me 3 times in last 2 weeks. My bill comes to either $70 or $71 and I hand the waitress a $100 (have 0 small bills on me) and she brings me back a twenty, a five, and five ones or when its $71, a twenty, a five, and four ones. What do we do?

I'd keep the $20 and leave the rest.

I'd ask to break the $20.

If they wanted more than a $10 tip then surely they would have already some that, right? I value my time a lot, even though 95% of jt is spent doing nothing and having to waste a few minutes on something like this tends to really irritate me.

Also if they keep getting under tipped in his spot perhaps they'll learn from their stupid mistakes and start brining two tens.

It's up to you, but I try to tip what I want to tip. The mistake has to be pretty stupid before I change my mind.

(Also I have two kids under 5 so I tip an amount what others may consider insane.)

I also don't tip on the tax, so with 9.25% around here, 15% tip comes out to $9.60 on $70 total.

If the service was really good, leave the fun tic and walk out. Otherwise, order a couple of desserts to go, then leave the fun tic.

Or, you could hand her the bill and say, "I'll need $15 back."

That much postprandial math causes indigestion.